ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 46, 19, 20 Manuilov, Vladimir, Moscow State University, Russia Almost representations of discrete groups and K-theory Let π be a discrete finitely presented group with generators g_{1}, …, g_{n} and relators r_{j}(g_{1}, …, g_{n}), j = 1, …, m. A set σ of finite-dimensional unitary matrices u_{1}, …, u_{n} is called an ε-almost representation of π if ∥r_{j}(u_{1}, …, u_{n})∥ ≤ ε. We discuss the following propery of π: for small enough ε every ε-almost representation σ generates a continuous path of ε_{t}-almost representations σ_{t} with ε_{t} → 0 while t → ∞ and ε_{t} ≤ δ(ε), where δ(ε) → 0 while ε → 0. We discuss also K-theoretical applications of almost representations of groups having the form π × Z.